adaptive downlink multi-user mimo wireless syfstems for correlated channels with imperfect csi
TRANSCRIPT
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 9, SEPTEMBER 2006 2435
Adaptive Downlink Multi-UserMIMO Wireless Systems for
Correlated Channels with Imperfect CSICheng Wang, Student Member, IEEE, and Ross D. Murch, Senior Member, IEEE
Abstract Multiple-Input Multiple-Output (MIMO) wirelessantenna systems provide increases in capacity without the needfor additional spectrum or power. However the capacity increaseis limited when the number of antennas at the receiver is fixedor restricted (due to mobile size constraints for example). Toovercome this limitation multi-user MIMO can be used, whichallows several users to be served simultaneously in frequency andtime. A disadvantage of these multi-user MIMO systems, when
used in the downlink however, is that they need accurate channelstate information (CSI) at the transmitter and also uncorrelatedchannels among users. In this paper we investigate methods toaddress the problems of multi-user MIMO systems in spatiallycorrelated channels. We adopt the concept of angle betweensubspaces to characterize the inter-user spatial correlation andadapt the algorithm to those conditions. We also investigatethe impact of the accuracy of CSI at the transmitter (CSIT)and whether more limited CSI such as channel correlationinformation alone can be used to provide good multi-user MIMOperformance. Results are presented as various simulated capacitymeasures and we use them to make comparisons between thevarious multi-user MIMO configurations.
Index Terms Multi user, MIMO, multi-user MIMO.
I. INTRODUCTION
MULTIPLE-INPUT Multiple-Output (MIMO) wirelesssystems provide increases in capacity without the needfor additional spectrum or power. It has been shown [1],
[2] that capacity grows linearly with the number of transmit
antennas provided that the number of receive antennas equals
or exceeds the number of transmit antennas in uncorrelated
Rayleigh fading channels. However, capacity grows much
slower as the number of transmit antennas increases when
the number of receive antennas is fixed or limited (due to
mobile size constraints for example), and in fact is bounded
[2]. Motivated by this limitation researchers have investigated
the possibility of multi-user MIMO (MU-MIMO) which can
serve several users simultaneously in frequency and time with
a particular focus on the downlink. It has been shown [9] that
by employing MU-MIMO techniques overall system capacity
can be increased significantly even when the number of receive
Manuscript received March 30, 2004; revised November 30, 2004 andAugust 4, 2005; accepted August 22, 2005. The editor coordinating the reviewof this paper and approving it for publication is M. Uysal. This work was
supported by the Hong Kong RGC grant HKUST 6149/03E.The authors are with the Department of Electrical and Electronic Engineer-ing, The Hong Kong University of Science and Technology, Clear Water Bay,Hong Kong (email: [email protected], [email protected]).
Digital Object Identifier 10.1109/TWC.2006.04202.
antennas at the individual mobile is limited to 1 or 2 in uncor-
related Rayleigh fading channels. However it is unclear what
effect fading correlation has on the spatial separability among
users [13] and consequently its effect on the performance of
MU-MIMO schemes. In addition MU-MIMO schemes need
channel state information (CSI) at the transmitter so that
appropriate signal processing can be performed to separate
multiple users in space. It is therefore important to consider
what types of CSI need to be available at the transmitter and
how accurate it needs to be.
In this paper we investigate methods to address the problems
of MU-MIMO systems in spatially correlated channels. In
particular, we adopt the concept of angle between subspaces
[3] to characterize the inter-user spatial correlation or users
spatial separability and use it to adapt the MU-MIMO schemes
to improve performance. We also investigate the impact of the
accuracy of CSI at the transmitter (CSIT). Two types of CSIT
are considered: instantaneous MIMO channel gain matrix and
also that consisting of the transmit correlation matrix only. Wefind that MU-MIMO algorithms exhibit different sensitivity to
CSIT accuracy in channels with different degrees of fading
correlation. For fairness consideration we use the minimum
capacity among simultaneous users as our performance mea-
sure. Simulation results demonstrate the gain achieved by our
adaptive algorithms.
Previous work on downlink multi-user MIMO systems has
suggested dirty paper coding (DPC) solutions [4], [5], [6], [7]
and it was recently shown in [8] that DPC in fact achieves
the full capacity region of the downlink multi-user MIMO
channel (MIMO BC). However due to the high complexity
of DPC implementation, low complexity sub-optimal schemes
with moderate performance degradation are desirable. Several
sub-optimal schemes have been formulated in [10], [11],
[12], [27], all take the similar approach of forcing the inter-
user interference to zero. Much of the emphasis in these
formulations has been on determining the potential advantages
of these approaches and they have therefore concentrated on
systems that assume perfect CSI is available at the transmitter,
and the channels are uncorrelated. In practice however strong
fading correlation between pairs of transmit antennas often
exists [14], [15], [16], and as we will see later that it will cause
the above formulations to fail to guarantee the instantaneousQoS provisioning, since in certain time interval some users
data rate might be unacceptably low. Also it is unclear what
CSIT and accuracy will be available at the transmitter. Our
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2436 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 9, SEPTEMBER 2006
work is different in that we focus on the impact of the channel
characteristics on the performance of MU-MIMO formulations
and suggest adaptive approaches to improve performance.
The remainder of the paper is organized as follows. In
section II, preliminaries are introduced, while in section III
a brief summary of several downlink MU-MIMO schemes
is provided. In section IV, inter-user spatial correlation is
analyzed and two adaptive algorithms are proposed. Section V
provides the numerical results. Finally, conclusions are drawn
in Section VI.
I I . PRELIMINARIES
A. Downlink Multi-user MIMO Transmitter Structure
We consider the downlink of a narrowband multi-user
MIMO system with M transmit antennas at the base station(BS) and Nk receive antennas at the k
th user. We denote
such a system as a M (N1, N2, . . . , N K) system, whereK is the number of users that the BS is communicating
with simultaneously in frequency and time. Let the Lk 1vector bk be the transmit data symbol vector for user k,where Lk is the number of parallel data streams transmittedsimultaneously to user k, k = 1, . . . , K . All these data symbolvectors are passed through certain transmit pre-processing
matrix Tk, k = 1, . . . , K , before they are launched into thedownlink channel. The received signal of user k can be writtenas
yk = Hk
Ki=1
Tibi + nk, (1)
where nk
N(0, I) is the additive white Gaussian noise
vector and I is the identity matrix.
B. Channel Model
The downlink channel for each user is modeled as a semi-
correlated NLOS Rayleigh flat fading channel, where it is
assumed that fading is correlated at the transmitter side but
uncorrelated at the receiver side [16], [17]. In this case, the
channel could be modeled as
Hk = GkAk, (2)
where Gk is a Nk Dk matrix with zero-mean unit-variancei.i.d complex Gaussain entries. Ak is the steering matrix ofsize Dk M containing Dk steering vectors of the transmitantenna array corresponding to Dk directions of departure(DOD). Consider a uniform linear array at the BS, the steering
matrix Ak is given by
Ak =1Dk
aT(k1), . . . , aT(kDk)T, (3)with
a() =
1, ej2d sin
, . . . , ej2(M1)d sin
,
where T represents the transpose operation, d is the equidistant
antenna spacing and is the carrier wavelength. With thismodel, angle spread can be modeled by a large number of
discrete DODs, and different degrees of transmit correlation
are adjusted by varying the angle spread. Throughout the paper
we denote a semi-correlated channel with D DODs randomly
and independently distributed in an angle spread as a (D, )channel.
The transmit correlation matrix is then given by
RT xk = E
HHk Hk
= NkAHk Ak, (4)
where H represents the complex conjugate transpose and E[
]
denotes expectation operation.
C. Channel State Information Accuracy
A time division duplex (TDD) system is assumed in this
paper. Two kinds of CSIT will be used, namely H-CSIT and
R-CSIT. By H-CSIT we refer to a transmitter that knows
the instantaneous channel matrix H. While by R-CSIT we
refer to a transmitter that only has the correlation matrix RT x
available.
The transmit correlation matrix is determined by the DODs,
which correspond to the scatterers angular position withrespect to the transmitter. The DODs do not alter rapidly for
small movements of the user [18] and as a consequence so
does the transmit correlation matrix. In most cases the BS
should be able to acquire the transmit correlation matrix [16],
[17], and throughout this paper we will assume if R-CSIT is
known to the BS, then it is accurate.
In contrast to RT x, the components of G describe the
complex path gains, whose phases and amplitudes change
much more rapidly even when the user moves slightly [18].
Since we assume a TDD system, the H-CSIT of the downlink
is estimated from the uplink. Therefore we assume the effect
of Doppler spread, which causes the uplink to be an inaccuratedownlink channel estimate due to the time separation between
them, dominates the error. Taking into account the fact that
DODs change much slower than the complex path gains, we
modify the model in [19] and quantify the problem as
H =
t G +1 2t GwA = t GA +1 2t GwA,(5)
where A is the steering matrix, H = GA is the estimatedchannel matrix,
1 2t GwA is the estimation error that
is uncorrelated with
H, t is the correlation coefficient
between the actual channel gain and its estimate, whichis assumed to be the same for all gains and is given by
t = E[hijhij ]E[|hij|2] E[|hij|2], where hij ,hij re-present the (i, j)th element of H and H respectively and denotes the complex conjugate operation. The entries of Gand Gw are all i.i.d zero-mean complex Gaussian with unity
variance. Thus 2h = 2h
= 1, and the variance of estimation
error is 1 2t . Users are assumed to be in a rich scatteringenvironment, which leads to t = J0(2fd), where J0() isthe zeroth-order Bessel function of the first kind.
III. MULTI-USER MIMO SYSTEMS
Various methods have been proposed for performing multi-
user MIMO communications. A summary of four multi-user
MIMO algorithms is provided here.
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A. MU-MIMO ZF Decomposition with Equal Power Alloca-
tion
In this scheme [10], Tk, k = 1, . . . , K is chosen such thateach user receives no interference from the other users, which
can be written in the form
Tk = VkWk, (6)
where Vk is an orthonormal basis of the joint null-spaceKi=1,i=kN(Hi) and can be computed by singular value
decomposition as
Hk =
HT1 , . . . , HTk1, H
Tk+1, . . . , H
TK
T=Uk Uk 00 0
VHkV
H
k
. (7)
Substitute (6) into (1), we get
yk = HkVkWkbk + nk. (8)We can see the multi-user MIMO system denoted by (1)
has been decomposed into K parallel single-user MIMOsystems. By thinking of the equivalent single-user MIMO
channel of user k as Hk = HkVk, the equivalent transmitpre-processing matrix should be chosen according to spatial
waterfilling [2] to maximize the mutual information subject
to the power constraint trace
WHk Wk
= PT/K, wherePT is the total transmit power. In this scheme the constraintM > max
krank
Hk
should be satisfied in order to ensure
the existence ofVk. A detailed description of this scheme can
be found in [10].
B. Max Average Transmit SINR Beamforming
In this scheme [18], transmit beamforming vector tk, k =1, . . . , K is computed by maximizing the average transmitSINR for each user, which is defined as the ratio of the average
desired signal power received at user k and the sum of theaverage interference and noise power introduced to the others
as follows
k =E
Hktkbk 2
Ki=1,i=k E Hitkbk 2 +Ki=1,i=k Ni , (9)where denots the Euclidean vector norm. We can see thatin this scheme each user tries to suppress its interference to
the other users and at the same time tries to transmit efficiently
to itself. By denoting tk =
Pkuk, where uk 2= 1, Pk =PT/K, the average transmit SINR can be further expressedas
k =uHk R
T xk uk
uHk
Ki=1,i=k R
T xi +
1Pk
Ki=1,i=k NiI
uk
, (10)
where we can see that only R-CSIT, i.e. RT xi , i = 1, . . . , K is need of.
To maximize k [18], it can be shown that uk should bechosen as the dominant generalized eigenvector of RT xk andK
i=1,i=k RT xi +
1Pk
Ki=1,i=k NiI
.
C. Max-Min Mutual Information MU-MIMO Scheme with
DPC
In MIMO BC [4], the dirty paper result suggests that
the transmitter encode the users data sequentially such that
through appropriate coding each user sees no interference
from the previously encoded users with full knowledge of
the signals to be transmitted to all the previously encodedusers in such a way that transmit power is not increased. As
a consequence, the mutual information for the two-user case
is given by
I1 = log2 det
I + TH1 HH1
I + H1T2T
H2 H
H1
1H1T1
I2 = log2 det
I + TH2 H
H2 H2T2
(11)
Since the encoding order is arbitrary, one can also achieve
mutual information
I2 = log2 detI + TH2 H
H2 I + H2T1T
H1 H
H2
1
H2T2I1 = log2 detI + TH1 HH1 H1T1 (12)The objective of this scheme is to select the non-zero pre-
processing matrices
T1, T2
, such that the minimum mutual
information IDP between the 2 users is maximized,T1, T2
= arg
(T1,T2)max IDP s.t.
2k=1
trace
TkTHk
= PT,
(13)
where I = min(I1, I2),
I = min(
I1,
I2), IDP = max(I,
I).
We discuss the numerical solution for this nonlinear optimiza-
tion problem in section V.
D. TDMA-MIMO
In this scheme, different users are separated in time, so there
is no inter-user interference. The mutual information of user
k is then given by
Ik =1
Klog2 det
I + THk H
Hk HkTk
, (14)
where the factor 1/K occurs because each of the K users onlyhas 1/K of the time for transmission due to time division.Tk is then chosen as the spatial waterfilling solution with a
total transmit power constraint, i.e. traceTHk Tk = PT tomaximize the mutual information according to [2]. If only R-
CSIT is available [16], it is optimal to transmit along the eigen-
vectors of RT x and a complicated numerical optimization is
needed to find the optimal power allocation. Since the solution
resembles waterfilling in the sense that stronger channel modes
get allocated more power, we use waterfilling to find a sub-
optimal power allocation for simplicity.
IV. ADAPTIVE MULTI-U SE R MIMO SYSTEMS
There are two problems caused by the channel that can
prevent MU-MIMO algorithms from operating well: spatialcorrelation among users and CSIT inaccuracy. Spatial corre-
lation among users prevents the separation of two or more
users in space and causes MU-MIMO algorithms to perform
poorly [13]. Inaccurate CSIT will have much greater impact
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on multi-user MIMO than on single-user MIMO because of
the presence of inter-user interference.
A key to overcome these problems is to realize that the
various MU-MIMO algorithms behave differently under differ-
ent channel conditions. For example when the users are highly
spatially correlated, TDMA-MIMO will probably perform
better than sub-optimal MU-MIMO algorithms. In addition,
the same MU-MIMO scheme may exhibit different sensitivity
to H-CSIT accuracy in channels with different degrees of
fading correlation.
Our approach here is to exploit the subspace structure
of the channel. By exploiting the subspace structure of the
channels of different users, we can identify when the inter-user
correlation is likely to cause MU-MIMO schemes to provide
poor performance and adapt them appropriately. By exploiting
the subspace structure of the channels of the same user, we can
investigate the sensitivity of MU-MIMO schemes to inaccurate
H-CSIT.
A. Spatial Correlation between Users
One key measure of the spatial correlation between users
is the relative orientation of the row-spaces of their channel
matrices. This is an indication of how independently the BS
can transmit to each user without affecting the other users.
Here, we suggest the use of the angle between the row-
spaces of users channel matrices to quantify users spatial
correlation. Through the analysis of the next subsection (IV.B),
we can gain some insight into the impact of this angle on sub-
optimal MU-MIMO schemes.
The concept of angle between row-spaces, or more gener-ally subspaces, can be found in [3] and a brief description is
as follows. Suppose Pand Q are two subspaces ofCn, Pand Q are their orthogonal complements respectively. LetP1 = [p1, . . . , pp], Q1 = [q1, . . . , qq ], P2 = [pp+1, . . . , pn]and Q2 = [qq+1, . . . , qn] be the orthonormal basis of thesefour subspaces respectively. Assume p q and p + q nwithout loss of generality [3], angle between P and Q canthen be computed as follows,
Step1, Calculate the SVD of PH1 Q1 as PH1 Q1 = XY
H,
or alternatively calculate the SVD of PH1 Q2 as
PH
1
Q2 = XYH
, where = diag(1, . . . , p),1 . . . p, = diag(1, . . . , p), 1 . . . p.
Step2, Calculate the largest principal angle = arccos(p)or = arcsin(1) as the angle between the twosubspaces Pand Q.
A small angle indicates that the two subspaces are nearly
linearly dependent. We apply this idea to MU-MIMO when
we have H-CSIT available at the BS and the resulting angle
will be referred to as angle between users or ABU. Forexample, ABU of user k and users {1, . . . , k1, k+1, . . . , K }can be computed by substituting the orthonormal basis of the
row-spaces of Hk, H
k into P1 and Q1. Note that for theABU of user k and the remaining users not to be alwayszero, the same constraint as needed in the MU-MIMO ZF
decomposition scheme, i.e. M > maxk
rank
Hk
, should be
satisfied.
When only the transmit correlation matrix RT x is available
at the BS, it is not possible to find the exact row-space of
the channel matrix H, however we can find the row-space of
RT x instead. In fact, it can be easily seen than the row-space
of H is a subspace of the row-space of RT x. So, when only
R-CSIT is available at the BS, ABU of user k and user jwill be computed by substituting the orthonormal basis of the
row-spaces of RT xk , RT xj into P1 and Q1.
B. Impact of ABU on MU-MIMO Schemes
To gain insight into the relationship between ABU and the
direction of departure path, we study the ABU between twousers when each user has only 1 DOD in space for the sake of
clarity. Since Hk = gkak, k = 1, 2, they can be decomposedas
Hk = kukvHk , (15)
where uk = gk/
||gk
||, vk = a
Hk /
M and k =
M
||gk
||.
The row-space of Hk is a one dimensional subspace spannedby vk, which is solely determined by ak . It can be easily
shown that
sin2 = 1 1
M2||aH1 a2||
2
=
1 1M2
1 cos
2 dM(sin1 sin2)
1 cos
2 d
(sin 1 sin2) 1 = 2
0 1 = 2
(16)
where 1 and 2 is the DOD of user1 and user2 respectively.Assume 1 and 2 are uniformly distributed in [
, +],
let Zmn = 2|m n|d/, by using a well known seriesexpansion cos(Z sin ) = J0(Z) + 2
k=1 J2k(Z) cos(2k),
we obtain
E[sin2 ] = 1 1M2
Mm=1
Mn=1
J20 (Zmn). (17)
We next consider the capacity as a function of ABU for both the MU-MIMO ZF decomposition with equal power
allocation scheme and the max average transmit SINR scheme.
i. MU-MIMO ZF decomposition with equal power allocation
schemeWe first consider the special case where there is only 1 DOD
in space for user k, k = 1, . . . , K , K M. Later we gene-ralize to the case for arbitrary number of DODs. For 1 DOD
case, we know that the row-space of Hk is a one dimensional
subspace determined by ak and the row-space of Hk in (7) is
a at most K1 dimensional subspace spanned by Vk, whichis solely determined by a1, . . . , ak1, ak+1, . . . , aK. Then wecan get the following results
cos2 k = vHk
Vk
VHk vk = ||vHk
Vk||2,
sin2 k = vHk VkVH
k vk = ||vHk Vk||2.(18)
where k is the ABU of user k and the remaining users.The equivalent single-user MIMO channel of user k can be
expressed as
Hk = HkVk = k ukvHk Vk = ukk sin(k)v
Hk , (19)
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where vHk = vHk Vk/ sin k, k =
M||gk||. Then we get
Tk =
Pk/KVkvk and consequently
Ck = log2
1 + 2k sin2(k)PT/K
, k = 1, . . . , K . (20)
From the analysis above we can see that Ck is a monotoni-cally increasing function of k, k [0, /2]. When k = 0,the capacity decreases to 0.For a more general case, i.e. without the 1 DOD constraint,the capacity achieved by MU-MIMO ZF decomposition with
equal power allocation scheme for user k is bounded by
log2
1 +
PTKNk
2kmk sin2 k
Ck
Nk log2
1 +PT
KNk2k1 sin
2 k
, k = 1, . . . , K , (21)
when rank
Hk rank(Hk ) < M, where mk is the rank
of Hk, k1 k2 . . . kmk > 0 are the non-zerosingular values of Hk.
Proof: See Appendix I.It is obvious that both the upper and lower bound of Ck,
k = 1, . . . , K are monotonically increasing functions of k,k [0, /2].
ii. Max average transmit SINR beamforming scheme
We assume k = 2 and each user only has 1 DOD in spacein this case. The exact SIR seen at the receiver is given by
SI R1 = SI R2 =
1 + M Psin2 2
/ cos2 . (22)
where P = PT/2.
Proof: See Appendix II.Both SI R1 and SI R2 are monotonically increasing func-
tions of , [0, /2]. When = /2, both users dont seeany interference from the other user.
For the capacity achieved in this case, through similar
derivations, we obtain
Ck = log2
1 +
||gk||2(1 + M Psin2 )2||gk||2 cos2 + 1/P M + (MP + 2) sin2
,
k = 1, 2. (23)
Denote the second term in the log operation as X, if wetake the derivative of X with respect to , the numerator ofthe result is
2P Msin cos
2||gk||2 + P M||gk||2 sin2 (1 + cos2 )
+2sin2 + P2M2 sin4 + 2P Msin4 +||gk||2P M
1
.(24)
Its easy to see that X is a monotonically increasingfunction of when (/4, /2). When (0, /4), itdepends on P, M and ||gk||2. Nevertheless, for a large rangechoice ofM and P, X is a monotonically increasing functionof for a much larger range than (/4, /2).
From the analysis it follows that ABU is closely related
to the achievable capacity of these sub-optimal MU-MIMOschemes. Small ABU roughly indicates low capacity. As we
show in section V that the probability of ABU to be small,
say less than 30, is about 10% for both the 1 DOD channeland the (50, 20) channel, we can expect that the capacity
achieved by these two schemes at less than 10% outage willbe poor in these two channels.
By using the ABU measure we propose two algorithms
that can adapt to the channel conditions to achieve improved
performance.
C. Adaptive MU-MIMO+TDMA AlgorithmThe motivation of this scheme is to take advantage of
TDMA when the users are highly spatially correlated while
maintaining the good performance provided by MU-MIMO
when the inter-user correlation is low. We use ABU as the
benchmark to determine whether to use TDMA or MU-
MIMO. Here we consider the two-user case to demonstrate
the approach. Note however that the approach is aimed at the
general situation where there is a large pool of users that are to
be served. In this situation we randomly select two users from
this large pool to perform the adaptive MU-MIMO+TDMA
algorithm. When this pair is served the MU-MIMO+TDMA
scheme will then move on to the next timeslot and randomlyselect another pair to serve until all have been handled.
The basic adaptation relies on calculating ABU and when
it is larger than a certain threshold we say these two users are
compatible and decide to use MU-MIMO. When the ABU is
smaller than the threshold, we decide to use TDMA instead.
Since our objective is to improve the capacity at low outage
probability without compromising the good performance at
high outage probability provided by sub-optimal MU-MIMO
schemes, the optimal threshold should be the one that yields
the maximum ergodic capacity. If the threshold is too small,
then even when the users are highly spatially correlated MU-
MIMO will still be used, which leads to poor performanceat low outage probability and consequently a decrease in the
ergodic capacity. However if the threshold is too large, which
means even when the inter-user spatial correlation is low
enough for MU-MIMO to achieve good performance TDMA
will still be used, clearly this leads to a decrease in ergodic
capacity as well. Thus the optimal threshold should be the one
that results in the maximum ergodic capacity.
When H-CSIT is available then MU-MIMO schemes such
as MU-MIMO ZF decomposition with equal power allocation
and TDMA based on instantaneous channel matrix may be
used. When only RT x is known and it is not of full rank,
then the max average transmit SINR beamforming and TDMAbased on RT x should be used. When RT x is of full rank,
TDMA should be used rather than the max average transmit
SINR scheme as we will see in section V that the latter is not
efficient in a channel with low fading correlation.
Also note that as previously mentioned our approach is
general and can be extended to any number of users by
randomly pairing up the users. We then assign a timeslot to
each user pair and then apply the adaptive MU-MIMO+TDMA
algorithm within each timeslot.
D. Adaptive MU-MIMO Grouping AlgorithmIn the previous subsection we introduce an adaptive algo-
rithm, which takes advantage of TDMA when ABU is too
small for sub-optimal MU-MIMO schemes to work efficiently.
Although performance improvement at low outage probability
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2440 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 9, SEPTEMBER 2006
can be achieved, this algorithm in some sense reacts to the
disadvantageous condition passively. While ABU cannot be
changed, we can react more actively by exploiting the multi-
user diversity to perform some adaptive user grouping, or
so-called adaptive timeslot allocation. That is rather than
randomly select users from the large pool of users, we can
select users that are compatible and thereby exploit multi-user
diversity. As a result users in the same timeslot will probably
have low spatial correlation and therefore higher capacity can
be achieved.
For the sake of simplicity, we constrain the number of
users in one group to be two. Assume there are 2L activeusers, our problem is how to divide these 2L users into Lgroups, each of which contains two users and occupies one
of the L timeslots. The problem can also be interpreted as:
there are N = C2L2 C2L22 ... C22L!
possible group arrangements,
which arrangement should be chosen. In total there are
M =
2L(2L1)2 mutual angles and each possible arrangement is
associated with a set of L angles, corresponding to the anglesbetween two users in each of the L groups. Denote the sets ofangles as 1, . . . , N with j =
j1, . . . , jL
. In order
to ensure fairness to all the users to some extent, our aim is
to select the arrangement with its minimum angle larger than
the minimum angle of all the other arrangements. That is
j = arg1jN
max min
j
= arg1jN
max min
j1, j2, . . . , jL
(25)
In case several arrangements have the same minimum angle,
then the one with the largest second minimum angle is chosen.This process will continue and repeat, if necessary, until
theres only one arrangement left. The algorithm is as follows,
Step1, Calculate the M mutual angles and sort them inascending order
a1,b1, . . . , am,bm, . . . , aM ,bM
,
where am and bm are user indices. Load all possibleN group arrangements into GAnew. Set m = 1.Step2, Backup GAnew as GAold. Discard group arrange-
ments which put user am and bm in the sametimeslot. Store the remaining group arrangements in
GAnew, set m = m + 1.Step3, Repeat step 2 until there is only 1 arrangement left
in GAnew. In case GAnew is empty, which meansseveral arrangements have the same minimum angle,
restore GAnew with GAold, set m = m + 1 and goback to step 2.
Note, the more active users there are the better the perfor-
mance, but as the number of users increases the complexity
of the algorithm increases too. By intuition, when the user
number reaches a certain value, the performance will reach a
certain limit, in which further increases in the user number
will not gain much. Say n-user adaptive grouping alreadyachieves satisfactory improvement, if the system has more
than n active users in total, we can randomly divide usersinto several clusters with n users in each, then within eachcluster perform the adaptive grouping according to the above
algorithm.
The group size K is not constrained to 2, however it should
satisfy the constraint M > maxk=1,...,K
rank
Hk
when H-CSIT
is available or M > maxk=1,...,K
rank
RT xk
when only R-
CSIT is available, where RT xk is defined similar to Hk , to
ensure there exists non-zero probability for the K users to becompatible. Say each group contains 3 users and there are 3Lactive users in all. Then there are 3 angles associated witheach group and the best group arrangement can be obtained
using the same 3 steps.
E. Impact of H-CSIT Accuracy and Fading Correlation on
MU-MIMO Schemes
One key aspect of MU-MIMO algorithms is their sensitivity
to inaccurate H-CSIT. As mentioned in section II.C the
primary reason for the inaccuracy is the delay between the
estimation of the CSI and its use. In this subsection we wish
to understand the impact of fading correlation on MU-MIMO
schemes sensitivity to H-CSIT accuracy. The impact of H-
CSIT accuracy itself is explored in the numerical simulationsection that follows.
To appreciate the impact of fading correlation on MU-
MIMO schemes sensitivity to H-CSIT accuracy we assume
that the BS treats the delayed version ofH, i.e. H, as the accu-rate H-CSIT and use it to calculate the transmit pre-processing
matrix as if the actual channel is H. We first considertwo extremes. When the channel is totally uncorrelated, the
elements of the channel matrix are all i.i.d complex Gaussian
random variables with zero mean and unit variance. Even a
small delay between estimation and its use will cause the
subspace structure of the channel matrix to alter significantly
and as a result the performance of MU-MIMO scheme will besignificantly degraded. However when there is only 1 DOD in
space for each user we can prove that the capacity achieved by
adaptive MU-MIMO+TDMA algorithm, adaptive MU-MIMO
grouping algorithm, both incorporated with MU-MIMO ZF
decomposition with equal power allocation scheme, will not be
affected by delayed H-CSIT as long as the relative geometry of
the propagation path remains unchanged, i.e. the DOD remains
the same.
Proof: From the analysis of section IV.B, we know that
the rank-1 channel matrix
Hk =
gkak, k = 1, . . . , K
can be decomposed as Hk = kukvHk , vk is solely de-termined by ak , Vk and Vk are solely determined bya1, . . . , ak1, ak+1, . . . , aK. As a result k, k = 1, . . . , K isalso uniquely determined by a1, . . . , aK.
For TDMA, since there is only one sub-channel for Hk,all the transmit power will be dedicated to this sub-channel
irrespective of the exact value ofk. Thus Tk = PTvk. Aslong as ak remains unchanged, capacity achieved by TDMA
will not be affected even if t = 0.For MU-MIMO ZF decomposition with equal power allo-
cation scheme, as we have shown in section IV.B that
Tk = PT/KVk VH
k vk/ sin k, k = 1, . . . , K . As long asa1, . . . , aK remains unchanged, the capacity achieved by thisscheme will not be affected even if t = 0.
Thus capacity achieved by adaptive MU-MIMO+TDMA
algorithm, adaptive MU-MIMO grouping algorithm, both in-
corporated with MU-MIMO ZF decomposition with equal
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100 80 60 40 20 0 20 40 60 80 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DOD of the second user
sin2(A
BU)
Fig. 1. sin2(ABU) in (16) with user 1 having a DOD of 0.
power allocation scheme, will not be affected as long as
a1, . . . , aK remains unchanged.
From this derivation we understand that a critical parameter
characterizing the impact of fading correlation on MU-MIMO
schemes sensitivity to H-CSIT is the amount of change in
the subspace of the channel matrix with different degrees of
fading correlation. This can be defined as the expected value
of the angle between the row-spaces of H and
H(t), where
H(t) is a delayed version of H with correlation coefficient
t as defined in II.C. We denote this as expected row-spaceangle or ERA. ERA provides a measure of the amount of newinformation contained in H(t). The smaller the angle the lessnew information in H(t), as a consequence the smaller theperformance degradation.
V. NUMERICAL RESULTS
Using numerical simulations we wish to demonstrate the
following:
The impact of fading correlations on users spatial sepa-rability
The performance of our adaptive multi-user algorithms
The impact of CSIT accuracy on MU-MIMO schemes in
channels with different degrees of fading correlation
In the simulation, 8 (2, 2) system is investigated. Uniformlinear array (ULA) is used at the BS with equidistant spacing
between antenna elements to be half a wavelength. Semi-
correlated channels with 50 departure waves and 5, 20, 75
angle spread are investigated. We assume the DODs are
randomly and independently distributed in the angle spread
according to uniform distribution. Users are assumed to berandomly and independently distributed in [, ] accordingto uniform distribution around the BS.
The capacity we refer to in this paper is the minimum
mutual information among the K users, where the mutual
0 10 20 30 40 50 60 70 80 9010
2
101
100
ABU in degrees
CDF
1DOD(50,20)(50,75)uncorrelated channel
Fig. 2. CDF of ABU between two users for different degrees of fadingcorrelation.
information of user k is given by
Ik = log2 det
I+THk HHk
I+Hk
Ki=1i=k
TiTHi H
Hk
1HkTk
,
(26)
The optimization problem in (13) involves two nonlinear
optimizations that need to be solved numerically, each of
which consists of2
k=1 2M Lk real variables since Tk, k =1, 2 is a M Lk complex matrix. A Sequential QuadraticProgramming (SQP) method [22] is used. Modifications aremade to the line search, where an exact merit function [23],
[25] is used together with the merit function proposed by [24]
and [26]. The line search is terminated when neither merit
function shows improvement.
To allow benchmarking we compare our algorithms to those
described in section III in the following figures. The notation
R-TDMA and H-TDMA correspond to TDMA using R-
CSIT and H-CSIT respectively. R-MU MIMO and H-MU
MIMO denote max average transmit SINR beamforming and
MU-MIMO ZF decomposition with equal power allocation
respectively. R-MU MIMO+TDMA is short for adaptive
max average transmit SINR beamforming+TDMA using R-CSIT, and H-MU MIMO+TDMA for adaptive MU-MIMO
ZF decomposition with equal power allocation+TDMA using
H-CSIT correspondingly.
We begin by investigate the characteristics of the inter-user
spatial correlation. The function sin2(ABU) in (16) is plottedin Fig. 1, where the DOD of one user is fixed at 0 and theDOD of the other user varies from 90 to 90. In Fig. 2,the CDFs of ABU between two users for different degrees of
fading correlation are shown. We observe that users spatial
separability pattern is quite different in channels with different
degrees of fading correlation. For the uncorrelated channel,
ABU is always relatively large, while for the 1 DOD case and(50, 20) case, ABU is less than 30 for 10% of the time.
In Figs. 3-5, the performance of the adaptive MU-
MIMO+TDMA algorithm is investigated for different angle
spreads. In Fig. 3 we provide a plot of the threshold versus
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2442 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 9, SEPTEMBER 2006
0 10 20 30 40 50 60 70 80 904
4.5
5
5.5
6
6.5
Ergodiccapacityperuserinbits/channeluse
Threshold in degrees
RTDMAHTDMARMU MIMOHMU MIMORMU MIMO+TDMAHMU MIMO+TDMA
Fig. 3. Ergodic capacity versus threshold for 8 (2, 2) system with a(50, 5) channel, PT = 15dB.
0 1 2 3 4 5 6 7 8 910
2
101
100
Capacity per user in bits/channel-use
CDF
RTDMAHTDMARMU MIMOHMU MIMORMU MIMO+TDMA, threshold=20HMU MIMO+TDMA, threshold=45Dirty Paper Coding
Fig. 4. Capacity CDF for 8 (2, 2) system with a (50, 5) channel, PT =15dB.
ergodic capacity for a (50, 5) channel and show that themaximum ergodic capacity can be achieved. In Figs. 4-5 we
provide capacity CDFs for the various algorithms when theoptimal threshold is selected under various channel conditions.
Both the figures show that the threshold chosen according
to the maximum ergodic capacity criterion indeed achieves
the desired performance, i.e. improve the low outage capacity
without compromising the good performance at high outage
probability. For a (50, 75) channel we observe similar re-sults although we havent shown here due to space limita-
tion and the optimal threshold is 60 and 45 for R-MUMIMO+TDMA and H-MU MMIO+TDMA respectively. Also,
from the flat part around the optimal threshold in Fig. 3, we
conclude that the performance of this adaptive algorithm is
not sensitive to the threshold in a range at least [5, 5].Note that the optimal threshold for the H-MU
MIMO+TDMA algorithm in channels with different degrees
of fading correlation is fairly constant. However, for R-MU
MIMO+TDMA algorithm, the optimal threshold increases as
0 1 2 3 4 5 6 7 8 9 10 1110
2
101
100
Capacity per user in bits/channel-use
CDF
RTDMAHTDMARMU MIMOHMU MIMORMU MIMO+TDMA, threshold=35HMU MIMO+TDMA, threshold=45Dirty Paper Coding
Fig. 5. Capacity CDF for 8 (2, 2) system with a (50, 20) channel,PT = 15dB.
0 1 2 3 4 5 6 7 8 910
2
101
100
Capacity per user in bits/channel-use
CDF
RTDMAHTDMA
RMU MIMOHMU MIMOR4 user groupingR8 user groupingH4 user groupingH8 user groupingDirty Paper Coding
Fig. 6. Capacity CDF for 8 (2, 2) system with a (50, 5) channel, PT =15dB.
the channel correlation decrease. A larger threshold indicates
TDMA should be used more often. Also according to our
simulation result, always using R-TDMA is a good choicefor a (50, 75) channel when only RT x is known. Onepossible explanation is: the less correlated the channel the
less efficient the max average transmit SINR scheme. In both
the figures, we also provide the performance of max-min
mutual information MU-MIMO scheme with DPC, denoted
as Dirty Paper Coding. We can see that the performance
gap between adaptive MU-MIMO+TDMA algorithm and
the one using DPC is large. Besides, one should note that
in general TDMA results in a loss of spatial dimension
compared to the other MU-MIMO schemes.
Figs. 6-7 provide performance comparison between H-
MU MIMO, R-MU MIMO before and after adaptive usergrouping for (50, 5) channel and (50, 20) channel. Thenotation R-n user grouping, H-n user grouping refers
to n-user adaptive grouping incorporated with max averagetransmit SINR scheme using R-CSIT and with MU-MIMO
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0 1 2 3 4 5 6 7 8 9 10 1110
2
101
100
Capacity per user in bits/channel-use
CDF
RTDMAHTDMARMU MIMOHMU MIMOR4 user groupingR8 user groupingH4 user groupingH8 user groupingDirty Paper Coding
Fig. 7. Capacity CDF for 8 (2, 2) system with a (50, 20) channel,PT = 15dB.
0 5 10 15 20 250
1
2
3
4
5
6
7
8
9
10
Capacityat10%outageinbits/channeluse
PT
in dB
RMU MIMOHMU MIMORMU MIMO+TDMA, threshold=20HMU MIMO+TDMA, threshold=45R8 user groupingH8 uer grouping
Fig. 8. Capacity at 10% outage versus PT for 8 (2, 2) system with a(50, 5) channel.
ZF decomposition with equal power allocation scheme using
H-CSIT respectively. We observe that the capacity in the area
from 1% outage to 20% outage has been dramatically im-proved. When compared to the adaptive MU-MIMO+TDMA
algorithm, we find that adaptive MU-MIMO grouping algo-
rithm works much better than the previous one, which is
because of the effective exploitation of the multi-user diversity.
So, when there is enough number of active users, adaptive
MU-MIMO grouping algorithm should be used, otherwise,
adaptive MU-MIMO+TDMA algorithm should be used to
avoid the severe inter-user interference in case users are
highly spatially correlated. In addition, we can see that 8-
user grouping already provides enough degrees of freedom
to achieve desired performance and the performance gap
between 8-user adaptive grouping and the one with DPC,whose complexity is much higher, is reduced compared to
Figs. 4-5. For a (50, 75) channel we observe similar resultsalthough we havent shown here due to space limitation. The
performance of 8-user grouping using H-CSIT is better than
00.10.20.30.40.50.60.70.80.9110
0
10
20
30
40
50
60
70
80
90
t
ERAindegrees
1 DOD(50,5)(50,20)(50,75)uncorrelated channel
Fig. 9. ERA versus t for 8 (2) system with channels of different degreesof fading correlation.
0 1 2 3 4 5 6 7 8 910
2
101
100
Capacity per user in bits/channel-use
CDF
HMU MIMOHMU MIMO when rho=0HMU MIMO+TDMA, threshold=45HMU MIMO+TDMA, threshold=45 when rho=0H8 user groupingH8 user grouping when rho=0
Fig. 10. Capacity CDF for 8 (2,2) system with a (50, 5) channel in thepresence of imperfect channel estimate, PT = 15dB.
adaptive MU-MIMO+TDMA algorithm, however even with
8-user grouping, max average transmit SINR still doesnt
work well in a (50, 75
) channel, which means max averagetransmit SINR scheme is not capable of effectively exploiting
the degrees of freedom provided by channels with low spatial
correlation for multi-user separation.
In Fig. 8 we show the performance of various schemes
in terms of capacity at 10% outage versus PT. From thefigure we can see that all the schemes, except the H-MU
MIMO, show similar performance when PT is low. As PTincreases, the performance gains obtained by exploiting the
ABU measure get more and more significant. For example,
at PT = 20dB the capacity at 10% outage achieved by H-MU MIMO increases from 2 to 5 and 7 bits/channel-use
by employing the adaptive MU-MIMO+TDMA algorithm andadaptive MU-MIMO grouping algorithms respectively.
In order to investigate the impact of fading correlation
on MU-MIMO schemes sensitivity to H-CSIT accuracy, we
provide simulations of ERA versus t for channels with
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2444 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 9, SEPTEMBER 2006
0 1 2 3 4 5 6 7 8 9 10 1110
2
101
100
Capacity per user in bits/channel-use
CDF
HMU MIMOHMU MIMO when rho=0.5HMU MIMO+TDMA, threshold=45HMU MIMO+TDMA, threshold=45 when rho=0.5H8 user groupingH8 user grouping when rho=0.5
Fig. 11. Capacity CDF for 8 (2, 2) system with a (50, 20) channel inthe presence of imperfect channel estimate, PT = 15dB.
different degrees of fading correlation in Fig. 9. As expected,
we can see that the less correlated the channel the larger the
ERA, which means the faster the channel subspace changes,
and as a consequence larger performance degradation for the
same value of t is expected. Figs. 10-12 confirm what wehave observed in Fig. 9, i.e. the less correlated the channel
the more sensitive is MU-MIMO scheme to inaccurate H-
CSIT. Also we observe that scheme with adaptive grouping
still achieves certain gain compared with the one without
adaptive grouping. One possible explanation is that when
choosing group arrangement, only the relative relationship of
the minimum angles of each possible arrangement matters,
rather than the accurate values of those angles. This relative
relationship is less sensitive to inaccurate H-CSIT, so the
users in the same timeslot will have potentially low spatial
correlation, and therefore inaccurate H-CSIT has less impact.
Another thing we observe from Fig. 9 is that large change in
ERA mainly occurs from perfect H-CSIT to small degradation
in t, and the part after that is relatively flat. We have tested,although havent shown here due to space limitation, that
for t changes from 0.6 to 0 for a (50, 20) channel, the
performances of all the three algorithms investigated in Fig.11, are nearly unchanged.
The impact of our investigation may be helpful in defining
MU-MIMO systems for different scenarios. For example in
[14], [15], measurement shows that transmit fading correlation
between the BS antenna pairs does exist for both the indoor
and outdoor scenarios. In an outdoor environment, typically
the BS is elevated above its surroundings, and only waves
transmitted within a small angle spread, e.g. 5, 10, canreach the mobile. In this scenario, max average transmit SINR
scheme with adaptive user grouping is preferred because it
only needs RT x, which can be estimated less often. In [14],
it is reported that in an indoor NLOS case, correlation betweentwo transmit antennas can be quite high as the distance
between the transmitter and the receiver increases. Also, since
the channel varies much slower than the outdoor case, high
quality channel estimation could be obtained. In this scenario
0 1 2 3 4 5 6 7 8 9 10 11 1210
2
101
100
Capacity per user in bits/channel-use
CDF
HMU MIMOHMU MIMO when rho=0.85HMU MIMO+TDMA, threshold=45HMU MIMO+TDMA, threshold=45 when rho=0.85H8 user groupingH8 user grouping when rho=0.85
Fig. 12. Capacity CDF for 8 (2, 2) system with a (50, 75) channel inthe presence of imperfect channel estimate, PT = 15dB.
the MU-MIMO ZF decomposition scheme with adaptive user
grouping is preferred.
VI. CONCLUSION
In this paper we investigated the effect of fading correlation
on MU-MIMO schemes. One effect is that fading correlation
heavily influences the spatial correlation pattern between co-
channel users. The more correlated the channel the more likely
users become highly spatially correlated. By adopting the
concept of angle between subspaces, two algorithms namely
adaptive MU-MIMO+TDMA algorithm as well as adaptiveMU-MIMO grouping algorithm are proposed in order to
increase the system capacity and ensure instantaneous QoS to
users. The other effect is MU-MIMO schemes show different
tolerance to inaccurate H-CSIT in channels with different
degrees of fading correlation. The more correlated the channel,
the less sensitive is the performance of MU-MIMO scheme
to inaccurate H-CSIT. Numerical results show that provided
perfect CSIT is available, both algorithms we propose are
capable of significantly improving the system capacity at low
outage by avoiding severe inter-user interference, with the
latter superior to the former because channel diversity in the
user domain is successfully exploited. For inaccurate H-CSIT,
the two algorithms we propose still achieve gains compared
with the original MU-MIMO ZF decomposition with equal
power allocation scheme.
APPENDIX I
Proof: First,we introduce two inequalities we will use in
the proof.
Proposition 1 ( [20]): Let 1(X) 2(X) . . . n(X)be the singular values of X, then
j (BA
) 1(B
)j (A
) and j (AB
) 1(B
)j (A
).(27)Theorem 1 ( [21]): For any positive definite n n matrix
S, det(S)
1n 1
ntrace
S
. (28)
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The capacity achieved by this scheme for user k is
Ck = log2 det
I + HkWkWHk H
H
k
, (29)
where trace
WHk Wk
= PT/K.From Theorem 1 we have
detI + HkWkWHk HHk
trace
I + HkWkWHk H
H
k
Nk
Nk, (30)
therefore
Ck Nk log2
trace
I + HkWkWHk H
H
k
Nk
. (31)
From Proposition 1 its easy to see that
trace
HkWkW
Hk H
H
k max
H
H
k Hktrace
WkW
Hk = PT
KmaxHHk Hk, (32)
then from (31) and (32) we get
Ck Nk log2
1 +PT
KNkmax
H
H
k Hk
. (33)
On the other hand, since the capacity is achieved by water-
filling over the eigenmodes of HH
k Hk , rather than allocating
all the transmit power to the dominant eigenmode, we have
Ck log2 1 + PTK maxHHk Hk. (34)Let rank
Vk
= lk , then rank
Hk
= rank
HkVk
min{mk, lk} Nk. Assume
HHk Hk =
Uk Uk 2k 0
0 0
UHkUHk
= Uk
2kU
Hk ,
(35)
where
2k =
2k1. . .
2kmk
then
HH
k Hk = VH
k HHk HkVk = V
H
k Uk2kU
Hk Vk. (36)
From Proposition 1, we have
max
HH
k Hk
max
V
H
k Uk
max
2k
max
UHk Vk
= 2k1 sin
2 k, (37)
therefore from (33) and (37) we obtain the upper bound
Ck
Nk log2 1 +
PT
KNk
2k1 sin2 k. (38)
From (36), by straight forward mathematical manipulation,
we obtain
trace
HH
k Hk
2kmk sin2 k. (39)
In addition, since
max
HH
k Hk
trace
HH
k Hk
rank
Hk
trace
HH
k Hk
Nk
,
(40)
together with (34) and (39) we get the lower bound
Ck log2
1 +PT
KNk2kmk sin
2 k
. (41)
APPENDIX II
Proof: Equation (10) in this case can be written as
1 =N1N2
uH1 aH1 a1u1
uH1
aH2 a2 +
1PI
u1,
2 =N2
N1
uH2 aH2 a2u2
uH2 aH1 a1 + 1PIu2 ,(42)
where P = PT/2. For this special case we have
u1 = 1
aH2 a2 +1PI1
aH1 ,
u2 = 2
aH1 a1 +1PI1
aH2 ,(43)
maximize 1 and 2 respectively, and 1, 2 are two scalarsused to normalize u1 and u2. By using (18) we can easily
obtain
1 = 2 = 1Mcos2 (M + 1/P)2 + Msin2
(1/P)2 . (44)
For the exact SIR seen at the receiver side, we have
S IR1 =tH1 H
H1 H1t1
tH2 HH1 H1t2
=21a1
aH2 a2 +1PI1
aH1 a1
aH2 a2 +
1PI1
aH1
22a2
aH1 a1 +1PI1
aH1 a1
aH1 a1 +
1PI1
aH2
. (45)
By straightforward mathematical manipulation and (18), we
get
a1
aH2 a2 +
1
PI1
aH1 a1
aH2 a2 +
1
PI1
aH1
=M2
1/P + Msin22
(M + 1/P)2(1/P)2, (46)
a2
aH1 a1 +
1
PI1
aH1 a1
aH1 a1 +
1
PI1
aH2
=M2 cos2
(M + 1/P)2, (47)
substitute (44), (46) and (47) into (45) we obtain
SI R1 = 1 + M Psin2 2 cos2 . (48)Similarly we get SI R2 =
1 + M Psin2
2cos2 .
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Cheng WANG (S03) received the Bachelors de-gree in Electronic Science and Engineering fromthe NanJing University, NanJing, JiangSu, China,where she graduated in 2002 and was ranked firstin the department. She is currently working towardthe Ph.D. degree in the Department of Electrical andElectronic Engineering, the Hong Kong Universityof Science and Technology, Kowloon, Hong Kong.
Her research interests include multi-user MIMOwireless communication systems, adaptive resourceallocation and cross-layer design and optimization.
Ross D. Murch (S85M87SM98) is a Pro-fessor of Electrical and Electronic Engineering at
the Hong Kong University of Science and Technol-ogy. His current research interests include multipleantenna systems, compact antenna design, MIMO,WLAN, B3G and Ultra-Wide-Band (UWB) systemsfor wireless communications. He has several USpatents related to wireless communication, over 150published papers and acts as a consultant for indus-try and government. In addition he is an editor forthe IEEE Transactions on Wireless Communications
and was the Chair of the Advanced Wireless Communications SystemsSymposium at ICC 2002. He is also the founding Director of the Center forWireless Information Technology at Hong Kong University of Science andTechnology which was begun in August 1997. He is the program Directorfor the MSc in Telecommunications at Hong Kong University of Scienceand Technology. From August-December 1998 he was on sabbatical leave atAllgon Mobile Communications (manufactured 1 million antennas per week),Sweden and AT&T Research Labs, NJ, USA.